The plant is a chamaecyparis. It's in a pot indoors.
I thought it started looking wrong so I took a photo.

This is what it should look like (at least approximately):


And this is how it looks. At the right angle you can see lots of tiny white things on it. The branches with the things on them seem more drooping and yellowish in color than the few that don't have them:

Looks to me as if you have some sort of mite infestation on there. A mild soapy water solution would be my first try on this. 1/2tsp. dish soap to a liter of water (and stronger is not better, soap is salty so the mild solution is best).

Spray all parts of the plant thoroughly, the soil surface and the pot. Leave it on for a little while, then rinse the plant with plain (lukewarm) water in the sink.

Repeat the treatment every few days for a couple of weeks to get the succeeding generations. The soap will kill the adult mites but more will hatch from eggs that are not harmed by the soap. So to finish them all off, you must repeat for a while. Then watch carefully to see if they return (there might be another plant that has them or they might be on something else around your house.