Can you give a more specific time and place? Colonization of the Americas in the 17th century was very different from, say, colonization of Asia in the 19th century. For example, France's colonization of Canada is generally seen as very light-handed compared to the Spanish in Mexico and they had a good relationship with the Native Americans. On the other hand, the French colonization of Indo-China was very brutal and resulted in decades of civil war.
I can't speak to the economic or cultural aspects, but maybe I can say something about constitutional, legal and institutional developments of the British empire.
One good thing that the British did was to establish representative institutions and legal institutions in most of their colonies, and to plant in them the systems of Common Law legal systems and British Victorian (post-Northcote-Trevelyan) administrative systems.
At first, these representative institutions were representative only in the most minimal sense: they were composed mostly of nominated or ex-officio members, represented only White settlers and perhaps some privileged sections of the native community, and had only consultative powers.
Different colonies progressed at different rates, and not always in a linear direction, but between the middle of the 19th and the middle of the 20th centuries, in most colonies two developments took place. Firstly, the composition of legislatures gradually became more democratic, with a reduction in the number of official or appointed members and an increase in the number of elected members, together with a gradual extension of the franchise. Secondly, there was a gradual move towards 'responsible government' with British-appointed governors increasingly handing over powers to ministers drawn from and responsible to these legislatures. Canada, Australia, South Africa and New Zealand completed this process by the third quarter of the 19th century. Other parts of the empire only reached that status of responsible government in the 1960s, in the years immediately before full independence, but the point is that wherever the British empire went, sooner or later, it created democratic institutions. It acculturated people into parliamentary democracy. It trained a class of 'native' leaders in the concept of free elections, the rule of law, government and opposition, the use of the ceremonial mace and the whig, and all the conventions, symbolism and pomp of the British system in its 'export model'. Not only were there native politicians, but native lawyers and judges too, who were similarly trained and acculturated.
The empire left behind ideas of government, politics, democracy, rule of law, and rights, which were embodied in post-independence constitutions. Since inclusive, effective, legitimate institutions are key to successful development, this was a real benefit. Obviously some countries benefited more from this than others, but overall I think the record of British colonialism in institution-building was pretty good, especially when you compare it to countries like France and Belgium which, as I understand it, did much less to prepare their colonial subjects for self-government.
Sources:
S. A. de Smith (1961) 'Westminster's Export Models: The Legal Framework of Responsible Government'.
Harshan Kumarasingham (2013) 'A Political Legacy of the British Empire: Power and the Parliamentary System in Post-Colonial India and Sri Lanka'.
W. I. Jennings (1958) 'The Approach to Self-Government'.