There are some supposals on what the "Tajik" word means. Many Tajiks theirselves, are sure, that the word comes from "taj"-crown. The etymology of the word is still subject of discussions, but according to historical sources, the word appeared after Arabs and Turks, who named as Tajiks local (Iranian) people.
In fact, Tajik people might be people of Tash-kurghan (China), who speak their own Sarikoli Language (belongs to East-Iranian language group), or people speaking Wakhi language at upper Hunza, or even Dards from Northern Pakistan. So, it's clear that Tajik means a group of people belong to Iranian race and speaking in different Iranian languages. However, the majority of Tajiks speak in Tajiki - a dialect of Persian, also known as Dari from mid-age literature. There are many dialects of Tajik (Persian) language in Tajikistan. As the process of transforming old local Iranian languages (Bactrian, Sogdian, Scythian, Khorezmian, Parthian and others) into Persian, was very dependent to some historical events. There is a big difference in lexicon and pronunciation. For instance, Tajiks from the North use many of Turkic words, at the same time people from some areas of Badakhshan speak in very archaic dialects, closed to Persian language of 9-10 century (AD). Moreover, dialects (languages) of Badakhshan (both in Tajik and Afghan sides) are so much different, that since 20th century these languages were named as Pamiri languages. There are 3 different language groups in Tajik Badakhshan: Yazgulami (Vanj district), Shughnan-and-Rushan dialects, Wakhi dialects in Ishakshim area and small number of people, speaking in Ryn language (Ishkashim district). An other language - Yaghobi, survived in Yaghnob valley of Fan Mountains.
This was a real sensation at the beginning of 20th century, when linguists found a dialect of Sogdian language, which was referred died Iranian languages.
There is no problem to communicate for Tajiks and Persians, as both have one literature language, but, usually, people speak on their own dialects and this might cause some misunderstanding when communicating. The difference between Tajik (Persian) and Pamiri languages is about the same as between present English and German. Present Persian (Tajik) lost its flactic
Modern Persian has many words come from Arabic in origin, at the same time the Tajiks have very strong influence of Russian language, though have more Iranian lexicon.
According to ancient Roman and Chinese sources, the ancient Iranians (Sogdians, Bactrians, Parthians, Khorezmians, Scythians
and others) at beginning of 3d century BC spoke in about the same dialects and understand each other.

The language of Avesta (the oldest written Iranian language, 10-7 century BC) was much closed to old Persian written in oldest Achaemenian writings. Since that time, in one thousand years, in time of Sasanids (a Persian dynasty, 3-7 century AD), the difference was big (Sogdians from Samarkand and Bukhara hardly understood Persian speaking people). At present,
Tajiks are majority in Tajikistan (about 65-70%), but there are also many Uzbeks (25%) and other nations live in the country. The rest are Russians, Kyrgyz, Turkmen, Tatar, Ukrains and other minorities. Many of people (especially Russian speaking citizens) left the country because of the civil war.