Answer:
You are a father talking to a man who wishes to court your daughter
Explanation (broken into parts):
Intro
You know who I am, and don't forget it. And don't forget what I'm telling you now: (the man wanting to court the daughter would at least be aware of the father's existence and would have reason to follow the father's council to stay on good terms with the family)
Lines 1-2
Years ago, I was in a similar place. So on this occasion I will treat you with grace (the father would have once courted his own wife and had to have dealt with his wife's father, so the father will have at least some understanding of the man's intentions)
Lines 3-4
You have adorned yourself to match my creation. But let’s not forget your lower station (the man has likely prepared himself to meet the father and appear worthy of the daughter, possibly by dressing up. The father considers the man to be of lower station than him in relation to the girl, considering he is the girl's father and the man has relatively little relation with the daughter up to this point)
Lines 5-6
Your hands are your own, and that much is clear. But the work they may do gives me reason to fear (The father is expressing concern that the man may intend to have a sexual relationship with his possibly young or sheltered daughter)
Lines 7-8
Keep them under wraps, and employ no device. No matter how much your mind is enticed (The father is instructing the man to avoid having a sexual relationship with his daughter despite temptations that exist)
Lines 9-10
I will use no tools to intimidate, My existence alone should make you hesitate (I, for one, have definitely heard of fathers hinting at threats with baseball bats or shotguns (tools) over their daughters, but this father appears to be different. In any case, if the man is young the father is likely intimidating even without tools. If the man is a bit older and has intentions of a serious relationship, he probably wants to stay on the family's good side.
Lines 11-12
When you return, it best not be late. For- know it now- alone I will wait (Don't keep my daughter out later than curfew, or whatever time you said you'd bring her back. If you do, the father will almost certainly be up worried and waiting, and likely very angry)
Lines 13-14
If you want memories more than regrets, Then do not think these idle threats (If you want a long lasting relationship where you can build memories together, you probably don't want to be going behind the father's back, who appears to believe he has the ability to prevent a relationship between the two (again, possibly because the daughter and suitor are both young))
Lines 15-16
Dance around the issue, but do no more, Or you’ll forever be met with a locked, closed door (if the man doesn't follow the father's council he will quite literally be met with a closed door when the father will prevent his daughter (who appears to be still living with the family) from seeing him)