Engineering can be considered the application of technology for the design and development of solutions to problems that often have a significant economic consequence to an organisation or community or society.
For example a civil engineer designing a bridge for people to cross has a high level of responsibility to ensure the safe and economic realisation of the success of the design.
A failure of the bridge (engineering disaster) could result in the injury or death of people and hence cause a negative economic impact on the community that relies on the bridge for the transfer of goods or people or information.
The American Engineers' Council for Professional Development in 1947, now called the Accreditation Board for Engineering and Technology, defined Engineering as:
The creative application of scientific principles to design or develop structures, machines, apparatus, or manufacturing processes, or works utilizing them singly or in combination; or to construct or operate the same with full cognizance of their design; or to forecast their behavior under specific operating conditions; all as respects an intended function, economics of operation or safety to life and property.
Which essentially means making useful solutions, based on known science principles, to problems without causing harm but within known limits of operation.
Other uses of the word engineer
On occasion people will use the word 'engineer' as a verb, to engineer something, is to find a solution to a problem or manipulate something. For example bioengineering generally means using biological principles to modify an organism.
One who practices engineering is called an engineer, and those licensed to do so may have more formal designations such as Professional Engineer, Designated Engineering Representative, Chartered Engineer, Incorporated Engineer, Ingenieur or European Engineer. The use of the term 'engineer' in a job title is sometimes controversial in some jurisdictions. But generally the term implies a high level of responsibility to the safety of infrastructures goods or data(especially in the IT sense)