Traditionally, all linguistic study was diachronic: all language study focused on language's change over time. For example, a predominant question asked in diachronic study is how did Old English transition to the very different Middle English to the different, yet similar, Modern English of Queen Elizabeth's time. For example, see the progress of Old English gieddian to Middle English singan to the uninflected Modern English sing. Or see the progress of the modern representation of a sleep vision (for which we now have no single word other than "dream" {OE drēam; ME dreem}) from Old English mǣting to Middle English sweven. It is clear there is much of interest in diachronic study.
The one thing it leaves out, however, is the interaction between language and society: it never asks Why changes occurred from a social perspective nor How society uses language or is affected by changes in it. The answers to these and similar questions lies not in the progress of language over time (diachronic) but in language and society interacting in a given set time (synchronic).
a) Synchronic study of language is the study of the interaction between language and society in a fixed time period. Therefore, synchronic language study answers these questions previously neglected by diachronic study. Therefore, the advantage to synchronic language study is that the social linguistic dynamics of a set time period may be discovered.
b) Additionally, the set time of synchronic study may be in the past or it may be in the present. Diachronic study can look only at the past. Consequently, while synchronic study may lead to attempts to predict future changes based on present dynamics, diachronic study can only poorly lend itself to attempts at predictions.
c) Synchronic studies focus on language as it exists at a particular point in time, without reference to its historical development. These studies can provide a detailed analysis of the structure, usage, and meaning of language, as well as its variation across different communities and contexts. Synchronic studies are particularly useful for understanding the workings of language in the present moment and for identifying patterns and regularities that may not be immediately apparent from a historical perspective.
d) Diachronic studies, on the other hand, look at language over time, tracing its development and evolution from its earliest origins to the present day. These studies can provide insights into the historical, cultural, and social factors that have shaped language over time, as well as the processes of change and innovation that have occurred within the language system. Diachronic studies can also reveal patterns of continuity and change in language use, and can help to identify the origins of linguistic features and their subsequent diffusion and spread.