ISO9001 = Quality Management. Good common sense business practices, understanding customer requirements and delivering against them, management direction, internal audits, continual improvement. Pretty much a foundation standard that can be built upon by other standards.
ISO20000 = IT Service Management - aka the "ITIL Standard". A prescriptive set of activities covering the effective use of IT, including change management, incident management, release management, financial management, information security etc. Very precise requirements = not the easiest to obtain.
ISO27001 = Information Security Management, a full framework for managing risks to an organisation's (and its customers') data. Identification of assets, risk assessment, control implementation, security training, security incident management etc. Pretty much a standard expectation for most work in 2015...