It's significantly better than it used to be even in the relatively recent past. Data-capable cell connections are ubiquitous throughout Havana, although you have to be fairly well off to be able to afford a plan that can use them. Wifi connectivity is more widely available, and there's tons of parks where there's official government wifi signals available (you have to buy a card for time).

It doesn't even begin to approach the connectivity of the U.S., but the internet isn't a totally foreign concept. (I can only speak for Havana though, no idea what's it like outside of the cities)