It is very difficult to see, since the photo is a bit blurry, but this looks to me like parsley. If an ID is important to you at this point, you can check the seeds. Parsley seeds are small and kind of football-shaped. Cilantro seeds are a bit larger and completely round.
Either way, you will definitely need to start with a new plant. Once parsley and cilantro are done flowering and seeding, they die.
If you want to reseed the pot, you can wait just a little bit longer until the seed heads on this plant are brown. You can then harvest the seeds, refill the pot with fresh soil, and plant the seeds. Obviously, this will be the least expensive option, but it will take quite awhile before you have a plant you can harvest from.
If you want parsley much quicker, you can pull this now, purchase a parsley plant and refill the pot right away.
One thing you might way to consider...if you have space for 2 pots of parsley, you could set up a system where you have continuous parsley without purchasing new plants. Since parsley are biennials, you can harvest leaves from them for one year. The second year they will go to seed like this one has. If you plant one pot with seeds this year and one pot with a purchased plant, you should have one pot that you can harvest from and one pot that is going to seed every year.