Vedic mathematics is a collection of techniques for various school-level problems in arithmetic and algebra, devised by Hindu cleric Bharati Krishna Tirthaji, and published posthumously in 1965. Tirthaji claimed to derive the techniques from the Vedas, but it is widely acknowledged that they bear no relationship to ancient scripture, and hence the term "Vedic" is inaccurate.
Advocates of Vedic maths make grand claims about its scope and significance. It has found its way into various school textbooks in BJP-ruled states, and is receiving support from the Narendra Modi government as part of a wider project to saffronise education.
Vedic maths has been criticised on a number of fronts. The techniques focus on rapid calculation, and lack generality, e.g., applying only to numbers with certain properties. They are presented as algorithms without comment on why they work, leaving students with no greater understanding. Most are routine to prove, and some are found in earlier texts.
An emphasis on Vedic maths leads to a popular perception that the rich and abstract structures of modern mathematics can be reduced to a set of "tricks" and "tips". It diminishes ancient India's contributions in mathematics, and leads to genuine scholarly work on mathematics in the Vedas being unfairly viewed with suspicion.
References: The Fraud of Vedic Maths by Hartosh Singh Bal. Several papers describing and critiquing Vedic maths by Professor of mathematics S. G. Dani.