This depends on whether you are talking about the Spanish imperialism that made the Philippines a Spanish colony for roughly 400 years or whether you are talking about the US imperialism that made the Philippines a US colony for a bit less than 50 years.
Spanish imperialism largely shaped modern Filipino culture. Filipinos typically have Spanish surnames (as I do, being of Filipino descent). They are typically Roman Catholic. There are many words in the Tagalog language that are Spanish. In addition, the Spanish created a system in which power was held in the Philippines by a few mostly Spanish families known as the "illustrados." Spanish imperialism, then, created a system of rule by a few elites and an overall culture that was influenced greatly by Spanish ways.
US imperialism had less of an impact, being so much shorter. The same families pretty much stayed in power and many of them continue to be important today. Most Filipinos speak a good deal of English because of the American legacy. There is a mixed attitude towards the US that is generally positive, but which did lead to a movement that forced the US to abandon its military bases in the Philippines.
In short, imperialism has pretty much made the Philippines what it is today both culturally and politically.