I would break this sentence into this:
In 连日来, "连日" means "few days", with a emphasis in succession; suffix "来", short form of "以来", can be translated as "for the period of".
In "人气火爆", "人气" actually means popularity instead of people; "火爆" literally means "fire and explosion", it was usually only used to describe a living thing, or the temper thereof, meaning he/she/it has a strong temper. Nowadays, "火爆" is adopted to describe popularity too, meaning very high popularity; and for this usage, an closely related term with the same meaning being "很火", literally "very fire".
However, take note that both "人气火爆" and "很火" are somewhat slangy terms, and I would not consider them as standard Chinese. And "很火" is usually used in mainland China and other Mandarin speaking countries. In Hong Kong, where the main spoken language is Cantonese, "很火" is not used at all.