Why do wages not equalize across space? In standard economic theory wages are simply prices on the labor market determined in equilibrium by the supply and demand of labor. Looking across space within countries it is however standard to find a relative large variation in local wage levels. At the same time labor is often very mobile again within countries.
For the United States of America the U.S. Census reveals that in 1990 four percent of white males age 25 to 34 moved across state lines, with the cumulative effect that almost a third of this group no longer resided in the state in which they were born.
When individuals move the supply of labor changes and one could expect wages to equalize based on the assumption that the migration itself was motivated by the one state offering higher wages than another. Seen in the light of this it can seem a little puzzling that spatial wage differentials nonetheless continue to exist. What are the main explanations offered by economic theory?
There are several explanations for this in the literature (the order does not necessarily reflect importance of each explanation).

Different Price Levels: Non-trivial portion of the wage differential is due to different price levels/cost of living. Once you adjust for different price levels and compare real wages gap narrows. This is obvious but since you do not mention in your question whether you are talking about real or nominal wages I thought it is useful to mention that.
Regional Institutional Differences: For example Blackaby and Murphy (1991) argue that inter regional real wage differentials are at least partially due to labour market institution heterogeneity (unionisation and the bargaining system). This applies especially to unions/federations like US where there can be large heterogeneity in regional laws &amp; regulations.
Regional Heterogeneity/compensating differentials: Even within one country the geography is usually heterogenous which creates opportunity for compensating differentials  (Farber and Newman, 1989). If you are offered two jobs that are same in all aspects but one job requires you to relocate somewhere to Alaskan wilderness and the other job requires you to relocate to some pleasant state with nice beaches you will likely be willing to accept lower salary from the job in nicer place because you are compensated by the fact that you are living in a nice place. Some regional differences could be also explained by agglomeration economics (e.g. urban vs rural areas have different economic implications), see for example Combes &amp; Gobillon (2015).
Worker Heterogeneity: The wages would only equalize among workers that are homogenous across all work relevant characteristics. However, people are different from each other and often people who are similar tend to cluster together. For example, would it be surprising to find that average wage in silicon valley is higher than average wage in some farming community? This would be just comparison of apples to oranges. Hence looking at average wages can be deceptive and research that takes into account worker heterogeneity find that the wage differentials shrink substantially (see Gerking and Weirick, 1983; Dickie and Gerking, 1987;  Farber and Newman, 1989 and Combes, Duranton and Gobillon, 2008).
Regional Differences in Human Capital: Workers are not just compensated for their labor but also get return for their human capital. Human capital endowments might differ across regions (perhaps due to regional differences in quality of education) leading to wage differentials (see Duranton and Monastiriotis, 2002; Motellón, López‐Bazo &amp; El‐Attar, 2011).

I think the above summarizes all the major factors but there might be some further ones as well for that you can see the sources above and ones cited therein.