However means all the same, despite what has just been said. However, it failed, however hard he tried, however you like.
As a connector it needs a full stop or a semicolon before it — joining two sentences with a comma and however is the commonest punctuation fault in English. It also means to whatever degree: however hard he tried. Note whatever and whenever, built with the same -ever, which generalises what it attaches to.
1adverbhoweverAll the same; despite what has just been said.
“The hotel was expensive; however, the view from our room was worth every penny.”
2adverbwhateverTo whatever degree.
“However hard he tried, he couldn't open the jar.”
Too few real examples of this word to estimate which sense is commonest.
however is a connecting word.
How plus -ever, a Middle English compound. Whatever, whenever and whoever are built the same way.
Middle English
however
English, today
however
From Middle English however, how-ever, how-evere; equivalent to how + -ever. Compare howsoever.
Etymology from Wiktionary, CC BY-SA