I noted that in conversational language and slang, English native speakers often use "you know". Should this phrase be understood as a question "do you understand what I'm trying to say?" or as an assertion "as you probably know"?
It's a bit more complicated:
..., you know,... inserted somewhat randomly is one of those typical "fillers" with little to no semantic content. In almost all cases the speaker could simply leave it out - but so they could do with well,.... erm.... etc.
Hint: There will often be a small break in the "flow" of the speech, a deep breath while the speaker unconsciously gathers their thoughts. All signs for filler words. Note that the Wikipedia article linked above explicitly lists "y'know" as an example.
In the few cases where "you know" really is significant,
- it will either come as a clearly recognizable question (even in spoken language you should be able to "hear" a question) being short for Do you know?
You know my sister? (possibly points to person)
- or as a statement (again: listen), being short for As you (probably) know...
You know I've been interviewing for that job - I'll start Monday!
Context is key, as usual.
"You know" frequently joins "ummm", "aaah", "I mean", "the thing is", "like" and numerous other expressions as a vocal pause for thought (to which some speakers seem addicted).
It is properly used at the end of a statement for emphasis or to seek a positive response.
While I agree with the answers already present that it's often used as a "filler" like "like" etc, I'll add another use which is to reduce perceived condescension when you're either adding context or background information.
For example "When you turn a computer off, you know, it takes a few seconds to shut down - well this new tablet computer doesn't!"
The "you know" here is being used to soften me telling my conversation partner something they probably already know, without implying that I'm teaching them the basics, in order for me to then add some further information to that background/contextual information.
It's also occasionally used to cut yourself short when you realize you're over-explaining the background information: in this context it's being used to mean "You get the gist, and you already understand what I'm talking about, so I'll get on with the rest of my sentence". This usage is usually used when you just need to get your conversation partner "onto the same page", eg to make sure they know vaguely what topic you're talking about.
These are both fairly subtle uses of the phrase, and frankly I wouldn't worry about it: they're mostly just an additional social skill relating to "judging your audience", in order to help conversations flow better.