There are actually a few different mechanisms for a trait to be dominant vs recessive.

When an allele causes loss of function of the protein it makes, that’s often a sign that it will be recessive. For example, brown eyes are dominant to blue eyes, because the allele for brown eyes makes a brown pigment in the iris of your eye, while the blue allele simply doesn’t make the brown pigment (there isn’t a blue pigment, blue eye colour comes from the structure of the eye and the blood vessels running through it, like the veins of a pale skinned person). In this case, the recessive blue phenotype is simply an absence of pigment, so it can easily be masked by one copy of the brown allele, making the pigment. You’d need two blue alleles to have blue eyes, but one brown allele will do.

Other times, it’s a bit more complicated. For some genes, “dose” or number of copies is important, making an allele that has a product effectively recessive to the loss-of-function mutation because not enough of the product can be made from only one copy. There are also cases of codominance and incomplete dominance.

Generally a gene for a dominant trait does something, and for a recessive one doesn't.

For example, a gene saying to put melanin in the iris of the eyes is going to be dominant- if you have one copy of it, you'll put melanin in your irises and have brownish eyes. All you need is one gene to do that to make that work.

Our genes contain instructions for making chemicals (proteins) that are used by our body to do stuff.

Our genes come in pairs - each member of a pair is called an "allele", which you can think of as a variant of the gene. Slightly different instructions for the proteins.

In some cases, a phenotype (an external characteristic) is determined by a single gene. Then, as you know, it might be that one allele is "dominant", and an alternative is "recessive". You only need one copy of a dominant allele to "express" that version of the protein, but you need two copies of the recessive one.

Here's one way that might work:

Suppose there's a version of the gene that produces a protein that makes a flower yellow. Without the protein, the flower will be white.

Let's call the allele that produces this protein Y.

Maybe there's a different version of Y which is "broken". The instructions it codes don't make the protein that makes flowers yellow. Maybe they make a protein that does something else, or maybe they make a protein that does nothing at all. Let's call that one y.

A plant might have two copies of Y, or two of y, or one of each.

If it has YY or Yy or yY, it's able to produce the protein, and so it has yellow flowers. The Yy ones might produce less of it, but that doesn't matter of the protein is like an "on/off" switch.

On the other hand, some plants have only yy, which means they can't produce the proteins, and so the flowers end up white.

So Y = "yellow flowers" is dominant, and y = "white flowers" is recessive, because the plant only needs one copy of Y to know how to make the protein that causes flowers to be yellow.

Type and number of copies generally express the phenotype. The recessive type, in nature, enrich with the adaptability the dominant behavior adoption by characterization and deactivation (still present\dormant) layer.

At its core, genes & DNA are blueprints for the assembly of proteins. Some proteins (often catalysts) are significant enough that their presence/absence will have an effect on the phenotype. Whether you have 1 or 2 working copies of those blueprints, they're enough to cause this dominance effect.

Keep in mind that most genetics is a bit more involved than 1 pair of genes broken down into binary pairs, but that's the brief mechanism

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This doesn’t cause traits to be one or the other, but it’s related to

1. How prevalent is that trait in a population?

And

2. Does that trait make the thing that has it more successful at passing down its traits* or less successful at it?

*”passing down traits” == “making babies”