Adaptation - an adjustment in natural or human systems to a new or changing environment. Adaptation to climate change refers to adjustment in natural or human systems in response to actual or expected climatic stimuli or their effects, which moderates harm or exploits beneficial opportunities.
According to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC, 2014), adaptation measures in cities are crucial for successful adaptation to climate change. Apart from the population, urban areas concentrate a high proportion of socio-economic activities and production of the greenhouse gases. The increasing risks associated with climate change impacts in urban areas affect vulnerability and can have widespread negative impacts on well-being (safety, health, income, and assets), as well as on the national economy, ecosystems and natural capital.
Source: http://www.ipcc.ch/publications_and_data/ar4/wg2/en/annexessglossary-a-d...

Adaptive capacity refers to the ability of a system, such as urban areas, to adjust to climate change to moderate potential damages, to take advantage of opportunities or to cope with the consequences.
Adaptive capacity consists of socio-economic indicators, such as access to technology and infrastructure, and also takes into account gender aspects, the institutional capacity and overall preparedness of the society that determines its capacity to cope with climate change impacts.
Source: http://www.eea.europa.eu/publications/urban-adaptation-to-climate-change