Thai is a language spoken by close to 40 million people as a first language and by over 80 million people in total. The great majority of Thai speakers living in Thailand.
The Thai language used to have another name. During colonial times, it was referred to as "Siamese" which was the language of the country "Siam" which was the name of the unified kingdoms of what is today central Thailand.
The word "Siam" (or "สยาม", "sà-yǎam" in Thai) is said to have its roots in Sanskrit "syama" which means "dark" and which might refer to the skin-color of the region's residents. Interestingly, the name of a closely related language to Thai, Shan is said to be derived from the same Sanskrit word.
In 1939, "Siam" changed its name to Thailand. This was a nationalist move made by a man called Luang Phibunsongkhram who wanted to reform the country and bring it closer to Western democracy. "Thai" actually means "free" in the Thai language, so "Thailand", in turn is "the land of the free".
The word has a double meaning, however, since the main ethnicity in Thailand is called the "Tai" people. So Thailand means "land of the free" as well as "land of the Tai people".
The Thai language, in turn, is referred to as "ภาษาไทย" which is pronounced "Phasa Thai" and which means "language of the free".
Other than "Thai" and "Siamese", the Thai language is also sometimes referred to as "Central Thai" referring to the fact that it's actually a regional language of the central regions of the countries. It is also referred to as "Standard Thai", namely because it's the variant of the Thai language that the Thai government has picked as the country's "official" language.
Other, wide-spread variants of the Thai language include Southern Thai and Northern Thai, which are actually relatively different from the Central Thai language and not always mutually intelligible.