I am a bit confused about skills in 5e. It seems to me that there are no more skills, and no more ranks. So for instance you no longer have acrobatics that you can add points to add you level. Am I missing something, can characters really not improve as they level, except by putting points in ability?
Players no longer place skill points in their skills. They do improve over time though, as the relevant ability score increases and the character's proficiency bonus increases over the levels. Because the proficiency bonus grows as well, a character will improve skills with which they are proficient over time. The character growth here is marked by their general increase in proficiency, which is applied to all ability checks for skills, all saves and all attacks with which they are proficient.
I believe the idea behind the proficiency bonus is that while a first level fighter is good at hacking away at something, a wizard is just as good at hitting someone with a spell attack. They are both good at what they do, whatever that might be, and they both improve at the same rate because the proficiency bonus is determined by total character level.