Alright is the informal way of writing "all right." It can stand in for "okay," like the sandwich you had for lunch that was just alright — it was neither great nor terrible.
In a nutshell, alright means "fine" or "satisfactory": "Are the kids alright on that Ferris wheel?" You can use it to show that you agree with something someone said: "Oh alright, I get it." This one-word spelling of "all right" is okay when texting with your friends, but don't use it when you are looking to impress, such as in a thank-you letter following a job interview.
