"I can't seem to X" means that the person speaking believes they cannot do X, but that may not necessarily be true. This type of phrase is typically used when someone has tried to do X, and being unsuccessful at doing X, they come to the conclusion that they cannot. "I can't seem to open this door" - I have been trying to open this door, but have been unsuccessful (I am NOT 100% certain that I CANNOT open this door) "I can't open this door" - I am unable to open this door. Keep in mind: People will often say "I can't do X", even though they really can. The "seem" just adds to the subjectivity. It's more natural to use it in songs to convey that extra meaning, even though in real life it's often implied.

Here is an extra part to the answer. The first two answers are correct. The word "seems" in a song is connected to the emotion of feeling like you can't do something yourself. You may have tried several solutions, but have not yet come up with the right answer. The other connection is one of defeat, where you can see someone else can do the thing (the "anything") but you can't. You ask yourself "Why can't I seem to do anything? They can, but I cannot" or "Why can't I seem to do anything right?"

"I can't seem to do anything" has a bit more nuance than "I can't do anything". "I can't seem to do anything" is saying that it feels like I can't do anything, whereas the other is saying that I actually cannot do anything. Hope this helps! :)