居る (いる) is ”to be”, “to exist” as a stand-alone verb, but also it forms continuous/progressive tense when combined another verb as [verb 連用形 + て + いる].
- 彼女は本を読んでいる -> She is reading a book
The same [verb 連用形 + て + いる] also serves as a participle (verb adjective).
- 錆びている自転車 -> A rusted, rusty, bicycle
Note both いる and ある mean “to be in the state of”, but いる is a neutral observation while ある suggests the state is a result of an intentional action.
- 戸が開いている -> The door is open (not clear if somebody left it open, wind opened it, etc.)
- 戸が開けてある -> The door is left open (on purpose)
- 花が咲いている -> Flowers are blooming (the flowers can be in the field, mountains and/or in a garden)
- 花が植えてある -> Flowers are planted (someone specifically planted them there)