Well, it can mean both. We use it both in a general sense of progress, but also about specific things that are an expression of progress, i.e. improvements or advancements. It literally means "step(s) forward" if that helps. A closer translation for improvements might be "förbättringar" (förbättra - to better, to improve).
This is a good explanation. I'd say that improvements isn't generally a great translation for framsteg: as Joel says, the normal translation of improvements is förbättringar. And the normal translation of framsteg is progress. However that other sentence you're referring to, albernegiraffe, is Små framsteg är också bra. And here we run into an interesting difference between how framsteg and progress work. In Swedish, framsteg is a countable noun, but progress in English is uncountable. This means that in order to keep the plural meaning of Små framsteg är också bra, you need to switch words in English, and then, improvements is suddenly the best word available. (advancements works too).