Typically an assistant can do any of the bits that don't directly require the main artist's distinctive drawing style, allowing the artist to increase production because they can move onto the next page while their assistants finish up stuff that takes a long time but doesn't need as high a level of skill to do.
Things you could have an assistant do:
Flatting: If your comic is line art and coloured digitally, you can get somebody to do the tedious process of filling in all the colours. Since just clicking the fill tool leaves an ugly fringe, to get the best result you need to select, grow the selection by a pixel or two, then fill, which is easy for even a non-artist to do, but takes a while. This is a classic "my significant other wants to help me make my comic" job to delegate. Flatters can either go off a colour chart, or they can just colour in any old colours because the neat fill separated by layers is the main thing.
Colours: Like flatting but requires more artistic skill and knowledge of colour because it usually involves some kind of shading and highlights and a mixture of carefully following a palette and improvising where necessary. This is commonly done by artists still making their way into the industry, but there are people who specialise as pro colourists out there.
Tone: Like the colourist job but for screentones. In some cases the artist might tell you what to put where, in which case, any person with decently steady hands can do this, but in others it may be up to the toner to also pick tones, in which case you need a pretty solid creative person because toning is really easy to do badly by choosing the wrong style or doing too much.
Inking: You need to be at least a pretty good draftsperson for this one, but your drawing style is less important than just your general steadiness of hand and sense for line weight and light-dark balance. How good the inker needs to be depends on how loose or tight the pencils the main artist does are. I've worked as an inker on a job before, and it does speed up making the pages significantly.
Blackfills: On a black and white comic that's produced traditionally by artists who like to use a lot of black, like say Mike Mignola... there can legitimately be a need for a person whose job is to just carefully fill in the blackfills with a pot of ink and a brush to save the inker time.
Lettering: Honestly I'd totally get an assistant to do this if I could! Doing the letters can easily take me an hour on a two page update because I need to decide where I'm putting my bubbles, put the dialogue in there, make sure the bubble has nice space around the letters, make a pleasing tail going to the character, and also there's sound effect text to do too... Ugh it can be a slog, and somebody fairly competent could definitely do this by just pasting in the dialogue from a script.
Backgrounds: This is where you definitely get into "your assistant needs to be a pretty damn good artist in their own right" territory. One example a lot of people might have on their comic shelf of a creator using a background artist is the final Scott Pilgrim book. O'Malley was on a really tight deadline because the movie was coming out, so he gave a job to a lesser known artist with a similar style because he knew the final book was going to have a lot of crowd scenes and things. Personally I don't think the style is a perfect match; the backgrounds in the earlier books were rougher and had more personality, but I can see the necessity of the move. A background artist needs to have an excellent sense of space and perspective to fit in with the foreground artist's drawings. Presumably the character artist would need to leave some kind of perspective guide for them. Despite being one of the hardest ways to collab and pretty rare in the industry, this is hilariously one of the most requested ones on this forum by baby artists who don't want to draw backgrounds because it's hard, like a small child who doesn't want to eat their greens. 
Promo: Get your assistant to put together promo images with cropped panels, character art, quotes and taglines etc and post on all the appropriate socials through official accounts. Sounds awesome to me. Loads of time saved!
Not an assistant job special mention:
Storyboarding: I see this requested on the forums, but I've never heard of it in my time in the western comics industry. I guess maybe this is a more east asian approach or a very new thing that's emerged in webcomics? Getting a person to draw out roughs of the panel compositions to make sure they clearly tell the story and have good variety of panel layouts and angles, then getting in an illustrator who has beautiful drawing skills, but not necessarily visual storytelling skills, to follow the sketches as a guide but draw them all pretty. It makes logical sense because it becomes more like the pipeline of a movie or animated show, but in western comics, the layout of a comic and composition of panels is the job of the main artist of penciller with maybe some input from the writer. I've definitely done a job similar to this when working on a (non-comic) book; the publisher had picked an artist, but they were quite inexperienced and tended towards rather... flat and conservative or unimaginative layouts, so I was brought in (uncredited) to draw roughs of how the illustrations should be laid out to add more energy, drama and tell the story better. I guess through this method you could do wild stuff like combine the incredible visual storytelling of somebody like Scott McCloud with an artist who has a style that's very appealing to a specific demographic... it's certainly an interesting approach!
Either way, it needs saying just in case, because I have seen people asking for "assistants" to do this on this very forum... this is NOT a job for an assistant. The visual storytelling of your comic is one of the most important elements of your comic, maybe even just the most important job full stop. Because this job is basically the equivalent of being The Director of the movie, or the Conductor of an orchestra; it's not a job for some rando. If anything, this person needs to be more highly trained and experienced than your artist.
