The adjective "contemporary" means occurring or happening in the present as opposed to the distant past or distant future. The expression "our contemporary history" would then mean the history of India that has to do with the present (political events that are talking place presently), near future (because the elections are inevitably going to happen and for that reason the author already thinks of them as part of India's history) and more specifically the very recent past of the country because the recent past of a country is closely connect with its present. That's why you can talk about the forthcoming Lok Sabha elections as part of India's contemporary history.
Of course, when you say "the history of a country", it implies that we are going to talk about events that happened in the past. In this case, the expression "contemporary history", if taken literally, makes zero sense because "contemporary" means related to the present. But that's only true if you think of this expression literally. In general, "contemporary history" is understood to mean "the history of something closely connected to its recent past, present and near future". How recent is recent and how near is near depends on the history of the political region you're talking about. For the countries that once comprised the USSR, the recent past and near future would be from the collapse of the Soviet Union up to the present moment plus all major political changes such as presidential elections that are going to happen in the near future.