TOEFL and IELTS are used to measure your English language skills. It's a requirement for English speaking countries (or courses where language of instruction is English). These exams are required from non native English speakers (countries where native language is not English: example India, China, South Korea, Taiwan, Nigeria, Germany, Middle Eastern Countries..etc).
Historically IELTS was popular in Europe, Australia and Canadian region, while TOEFL was popular in USA.
Now both are widely accepted in most universities (so as a student you may not have to give both tests).
Above data was based on research conducted by ets.org.
Generally universities have strong cutoff (or minimum score) for TOEFL and IELTS. You have to make sure you meet those requirements.
Generally IELTS of 6.5 or toefl score of 79 is acceptable for most universities (individual departments may have their own requirements.