Education and Learning: This is the most common context for a learner. Teachers, parents, and students constantly talk about 打好基础 (dǎ hǎo jīchǔ) - “to build a good foundation.” It's used for any subject: math, English, or Chinese itself.
Economy and Development: In news and official reports, you will frequently encounter 基础设施 (jīchǔ shèshī), which means “infrastructure” (e.g., roads, railways, power grids). A country's economic development is seen as resting upon its `基础设施`.
Relationships and Arguments: `基础` can describe the basis of a relationship (e.g., trust, mutual respect) or the basis of an argument (e.g., facts, logic). It defines the core upon which the relationship or argument is built.
As a Modifier: It can be used before another noun to mean “basic” or “foundational,” as in 基础知识 (jīchǔ zhīshi) - “foundational knowledge.”