The particularly red/blue states are where this matters the most. Imagining a state with 10 districts and a split of 80-20 along party lines (and this is relatively as extreme red/blue you can get; americans aren't that homogenous). Ideally you'd expect that state to send and 8 - 2 split to the house of representatives to best represent their population. With gerrymandering it's trivial to insure those 20% are silenced as far as federal influence is concerned. That's a lot of people and, I would argue, not an ideal situation.
Note that if the people are literally just randomly red or blue like this in an 80:20 split across the state, it actually takes a LOT of work to ensure you get an 8:2 split of ten representatives out of that and you'd expect 10:0 instead if representatives are one-per-district.
One fix is to use multi-representative districts, e.g. you draw only two districts in that 10 member state, and in each district people are voting for _five_ representatives. If there are parties you can use this thing called the Jefferson system (yes named after that Jefferson) to pick members of parties to fill those five seats per district with a single vote per person in a fair way. We can expect that in this 80:20 scenario each district would send one minority party member and four majority party members. The way Jefferson works, getting five out of five members is going to need you to really _crush_ your opponents, because in effect for that last seat every vote helps them five times more than you - even "useless" votes like somebody who wrote in "Michelle Obama" make it harder for them to win that last seat.
In reality though things aren't that conveniently mixed. Most likely an 80:20 state has very different ratios in its big cities than in rural agricultural land, or on an Indian reservation, or between a college town and an otherwise similar town with no students. Gerrymandering is about drawing lines on a map so that say 40% of the people in one district are blue, even though it's 20% state wide, whereas maybe if you'd just "naturally" put the line around the big city it'd be 56% blue and they'd get a blue representative. This feels intuitively unfair, and it's frustrating that a Supreme Court felt able to say well, too bad, we don't "know" what fair even is.
Presidental and Senatorial, yes. For the House, those red districts in blue states and vice versa can help influence the majority.
At the state level, it depends on the number of districts. Some states are at large (one district) so it doesn't matter greatly, and on the other end of the spectrum you have places like Texas and Cali where there's so many districts that it would be hard to affect. But if you hit that sweets spot of like 2-5 districts (which represents 15 states) than the Map could have a huge effect on things.
