What is meant by the terms price elasticity, cross-price elasticity and income elasticity?

Each of these is an economic term related to the relationship between price and demand. Price elasticity is the simplest. It basically refers to the amount that demand for a good or service will change as price changes. If people are still willing to buy a good or service irrespective of price increases, then it is called "demand inelastic." If not, we say that it has a high demand elasticity.
Income elasticity is the relationship between one's income and one's demand for a good or service. A good or service (like electricity, for example) that is essential would still be in demand irrespective of one's income, and we would say that the good or service was income inelastic. The reverse is true for goods that only people with high incomes are willing to buy.
"Cross-price" elasticity measures changes in demand relative to prices of other, similar goods. For example, cable and satellite television can be quite expensive, and in a free market they might be forced to lower their prices if other, similar services (streaming television, for example) could be provided at a lower price.
https://www.investopedia.com/terms/c/cross-elasticity-demand.asp

https://www.investopedia.com/terms/i/incomeelasticityofdemand.asp

https://www.investopedia.com/terms/p/priceelasticity.asp